1. The Income-Expenditure Model
Economics
NINTH EDITION
Chapter 11
The Income-Expenditure Model
Prepared by Brock Williams

2. Learning Objectives 11.1 Discuss the income-expenditure model.
11.2 Identify the two key components of the consumption function.
11.3 Calculate equilibrium income in a simple model.
11.4 Explain how government spending and taxes affect equilibrium income.
11.5 Discuss the role of exports and imports in determining equilibrium income.
11.6 Explain how the aggregate demand curve is related to the income-expenditure model.

3. 11.1 A SIMPLE INCOME-EXPENDITURE MODEL (1 of 3)
Equilibrium Output
At any point on the 45° line, the distance
to the horizontal axis is the same as the distance to the vertical axis.

4. 11.1 A SIMPLE INCOME-EXPENDITURE MODEL (2 of 3)
Equilibrium Output
At equilibrium output y*, total demand y* equals output y*.
Planned expenditures
Another term for total demand for goods and services.
Equilibrium output
The level of GDP at which planned expenditure equals the amount that is produced.
equilibrium output = y* = C + I = planned expenditures

5. 11.1 A SIMPLE INCOME-EXPENDITURE MODEL (3 of 3)
Adjusting to Equilibrium Output
Equilibrium output (y*) is determined at a, where demand intersects the 45° line.
If output were higher (y1), it would exceed demand and production would fall.
If output were lower (y2), it would fall short of demand and production would rise.

6. 11.2 THE CONSUMPTION FUNCTION (1 of 3)
Consumer Spending and Income
Consumption function
The relationship between consumption spending and the level of income.
Autonomous consumption The part of consumption that does not depend on income.
Marginal propensity to consume (MPC) The fraction of additional income that is spent.

7. 11.2 THE CONSUMPTION FUNCTION (2 of 3)
Consumer Spending and Income
The consumption function relates desired consumer spending to the level of income.

8. ▼FIGURE 11.5 Moments of the Consumption Function

9. 11.2 THE CONSUMPTION FUNCTION (3 of 3)
Changes in the Consumption Function
Two factors that can cause autonomous consumption to change:
Increases in consumer wealth will cause an increase in autonomous consumption.
Increases in consumer confidence will increase autonomous consumption.

10. APPLICATION 1
FALLING HOME PRICES, THE WEALTH EFFECT, AND DECREASED CONSUMER SPENDING
APPLYING THE CONCEPTS #1: How do changes in the value of homes affect consumer spending?
Home equity is the difference between the home value and what is owed on the mortgage.
The largest component of net wealth for most families.
Changes in home equity like other forms of wealth affect consumer spending.
From 1997 to mid-2006 housing prices rose by about 90 percent and consumer wealth grew by $6.5 trillion.
This ended in 2006 as housing prices began to fall.
According to a review of studies by the Congressional Budget Office, each $1 decline in consumer wealth would lower consumption spending between $.02 and $.07, or $21 to $72 billion of spending.
This would reduce economic growth 0.1 to 0.5 percent during 2007.

11. 11.3 EQUILIBRIUM OUTPUT AND THE CONSUMPTION FUNCTION (1 of 4)
Equilibrium output is determined where the C + I line intersects the 45° line.
At that level of output, y*, desired spending equals output.

12. 11.3 EQUILIBRIUM OUTPUT AND THE CONSUMPTION FUNCTION (2 of 4)
Saving and Investment
Savings function
The relationship between the level of saving and the level of income.
S = y − C
y = C + I
y − C = I
S = I

13. 11.3 EQUILIBRIUM OUTPUT AND THE CONSUMPTION FUNCTION (3 of 4)
Saving and Investment
Equilibrium output is determined at the level of output, y*, where savings equals investment.

14. 11.3 EQUILIBRIUM OUTPUT AND THE CONSUMPTION FUNCTION (4 of 4)
Understanding the Multiplier
When investment increases from I0 to I1, equilibrium output increases from y0 to y1.
The change in output (Δy) is greater than the change in investment (ΔI).

15. APPLICATION 2 MULTIPLIERS IN GOOD TIMES AND BAD
APPLYING THE CONCEPTS #2: Are multipliers for government spending higher during recessions?
A common belief is that fiscal multipliers are larger during recessions, when there is more slack in the economy. But, it is quite difficult to estimate government multipliers accurately.
Valerie Ramey and Sarah Zubiary find no evidence of greater multipliers during slack times in the U.S.
Daniel Riera-/Crichton, Carlos Veigh, and Guillermo Vuletin found different results. By carefully looking at periods when both government spending increased and the economy had slower or negative growth, they found the multiplier to be This is larger than conventionally calculated multipliers.

16. 11.4 GOVERNMENT SPENDING AND TAXATION (1 of 5)
Fiscal Multipliers
Planned expenditures including government = C + I + G

17. 11.4 GOVERNMENT SPENDING AND TAXATION (2 of 5)
Fiscal Multipliers
The consumption function with taxes is
The formula for the tax multiplier is

18. 11.4 GOVERNMENT SPENDING AND TAXATION (3 of 5)
Using Fiscal Multipliers
Although it is very simple, our income-expenditure model illustrates some important lessons:
An increase in government spending will increase total planned expenditures for goods and services.
Cutting taxes will increase the after-tax income of consumers and will also lead to an increase in planned expenditures for goods and services.
Policymakers need to take into account the multipliers for government spending and taxes as they develop policies.
In the long run, of course, we are better off if government spends the money wisely, such as on needed infrastructure such as roads and bridges. This is an example of the principle of opportunity cost.
PRINCIPLE OF OPPORTUNITY COST
The opportunity cost of something is what you sacrifice to get it.

19. APPLICATION 3 THE BROKEN WINDOW FALLACY AND KENSESIAN ECONOMICS
APPLYING THE CONCEPTS #3: How does Keynesian Economics change our normal ideas of economic scarcity?
Austrian economist, Henry Hazlitt, popularized the “Broken Windows” fallacy in economics. Imagine that a hoodlum threw a brick through a store window. While at first this seems to be a tragedy, the store owner has to hire a firm to fix the window. That generates business for the window repair firm and, through a multiplier, additional business throughout the community. Was the broken window good for society?
The fallacy here is that the money that the store owner paid to have the window repaired would have been spent elsewhere in the economy, say on clothing.
Hazlitt applies a similar argument to public spending financed by taxes. A government spending program may appear to increase business, but the taxes needed to finance the spending—either paid now or in the future—will mean less business for other firms. Government spending and the taxes necessary to finance it will just crowd out other production of goods and services in the economy.
But in the Keynesian world, where resources are underemployed, the story is quite different. Here the increase in spending—even financed by taxes—will bring resources that are not being utilized into the economy. As long as there is excess capacity in the economy, the extra spending will increase output and not crowd out other goods and services.

20. 11.4 GOVERNMENT SPENDING AND TAXATION (4 of 5)
Understanding Automatic Stabilizers
After World War II, fluctuations in GDP growth became considerably smaller.
SOURCE: Angus Maddison, Dynamic Forces in Capitalist Development (New York: Oxford University Press, 1991); U.S. Department of Commerce.

21. 11.4 GOVERNMENT SPENDING AND TAXATION (5 of 5)
Understanding Automatic Stabilizers
C = Ca + b(1 − t)y
adjusted MPC = b(1 − t)
An increase in tax rates decreases the slope of the C + I + G line.
This lowers output and reduces the multiplier.

22. 11.5 Exports and imports (1 of 2)
To modify our model to include the effects of world spending on exports and U.S. spending on imports, we need to take two steps:
Add exports, X, as another source of demand for U.S. goods and services.
Subtract imports, M, from total spending by U.S. residents. We will assume that imports, like consumption, increase with the level of income.
M = my
Marginal propensity to import
The fraction of additional income that is spent on imports.

23. 11.5 Exports and imports (2 of 2)
Output is determined when the demand for domestic goods equals output.

24. ▼FIGURE 11.13 How Increases in Exports and Imports Affect U.S. GDP

25. APPLICATION 4
THE LOCOMOTIVE EFFECT: HOW FOREIGN DEMAND AFFECTS A COUNTRY’S OUTPUT
APPLYING THE CONCEPTS #4: How do countries benefit from growth in their trading partners?
From the early 1990s until quite recently, the United States was what economists term the “locomotive” for global growth.
Our demand for foreign products increased.
U.S. imports increased along with output during this period.
The increased demand fueled exports in foreign countries and promoted their growth.
Studies have shown that the increase in demand for foreign goods was actually more pronounced for developing countries than for developed countries.
Conclusion: The United States was truly a locomotive, pulling the developing countries along.

26. 11.6 THE INCOME-EXPENDITURE MODEL AND THE AGGREGATE DEMAND CURVE (1of 2)
As the price level falls from P0 to P1, planned expenditures increase, which increases the level of output from y0 to y1. The aggregate demand curve shows the combination of prices and equilibrium output.

27. 11.6 THE INCOME-EXPENDITURE MODEL AND THE AGGREGATE DEMAND CURVE (2of 2)
As government spending increases from G0 to G1, planned expenditures increase, which raises output from y0 to y1. At the price level P0, this shifts the aggregate demand curve to the right, from AD0 to AD1.

28. KEY TERMS
Autonomous consumption Consumption function Equilibrium output Marginal propensity to consume (MPC) Marginal propensity to import Planned expenditures Savings function

29. APPENDIX a FORMULAS FOR EQUILIBRIUM INCOME AND THE MULTIPLIER (1 of 9)
Formula for Equilibrium Output 1 2 3 4 5

30. APPENDIX a FORMULAS FOR EQUILIBRIUM INCOME AND THE MULTIPLIER (2 of 9)
The Multiplier for Investment
For the original level of investment at I0, we have
For a new level of investment at I1, we have

31. APPENDIX a FORMULAS FOR EQUILIBRIUM INCOME AND THE MULTIPLIER (3 of 9)
The Multiplier for Investment
Substituting for the levels of output, we have

32. APPENDIX a FORMULAS FOR EQUILIBRIUM INCOME AND THE MULTIPLIER (4 of 9)
The Multiplier for Investment
Finally, because (I1 − I0) is the change in investment, ΔI, we can write

33. APPENDIX a FORMULAS FOR EQUILIBRIUM INCOME AND THE MULTIPLIER (5 of 9)
Another Way to Derive the Formula for the Multiplier
The term in parentheses is an infinite series whose value is equal to
Substituting this value for the infinite series, we have the expression for the multiplier:

34. APPENDIX a FORMULAS FOR EQUILIBRIUM INCOME AND THE MULTIPLIER (6 of 9)
Government Spending and Taxes

35. APPENDIX a FORMULAS FOR EQUILIBRIUM INCOME AND THE MULTIPLIER (7 of 9)
Government Spending and Taxes
Using this formula and the method just outlined, we can find the multiplier for changes in government spending and the multiplier for changes in taxes:

36. APPENDIX a FORMULAS FOR EQUILIBRIUM INCOME AND THE MULTIPLIER (8 of 9)
Balanced-Budget Multiplier

37. APPENDIX a FORMULAS FOR EQUILIBRIUM INCOME AND THE MULTIPLIER (9 of 9)
Equilibrium Output with Government Spending, Taxes, and the Foreign Sector